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Thread: Simple-ish word problem

  1. #1 Simple-ish word problem 
    Forum Ph.D. verzen's Avatar
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    Trying to figure out this word problem. Its two people are painting a fence. One person can paint a fence in 6 hours, the second can paint it in 8 hours. After two hours, the first goes fishing and leaves the second to finish the fence. How long does it take the second to finish the fence?

    x -----x
    - + - = 1
    6 -----8

    Turns out to be

    --20
    2 -
    --14
    To finish the entire fence together.


    Now this is where I am stuck. I assume you take away the 2 (which equates to hours) which leaves 20 over 14 but what do you do after that?

    Thanks for the help.


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  3. #2  
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    I didn't really understand your notation, but:
    The first person is painting at 1/6 of a fence per hour. The second at 1/8 of a fence per hour. The first person paints 1/6 of a fence per hour times 2 hours. The second person paints 1/8 of a fence times 2+x hours. In sum they paint one fence. so
    (1/6)*2+(1/8 )*(2+x)=1
    Solve for x.


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  4. #3  
    Forum Ph.D. verzen's Avatar
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    Thanks Harold. Is the answer 3 and 1/3rd hours to finish painting the fence? (So the fence would take 5 and 1/3rd hours total to paint.)
    "Democracy is a problem because it treats everyone as equals." - Betty Fischer

    "back in the 50's or 60's Nicky Criuz was a gang leader who met David Wilkerson in New York City. After much discussion over months or years, i forget how long, Wilkerson's wife became pregnant. one day Cruz decides to test God, he basically prayed--God if you are real let the baby be born a boy-- it was a boy. "
    - Logic of a creationist

    Quod gratis asseritur, gratis negatur
    ""What can be asserted without reason, can be dismissed without reason. ""
    Reply With Quote  
     

  5. #4  
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    Quote Originally Posted by verzen
    Thanks Harold. Is the answer 3 and 1/3rd hours to finish painting the fence? (So the fence would take 5 and 1/3rd hours total to paint.)
    Yes, that's what I get.
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  6. #5  
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    Take the sum of the percent (as a decimal) of how much they can paint in an hour. This would be the equivalent of , now multiply by how long they work before person number one stops, which would be . Now we know that the fence has been requires of his total percentage left to paint. We divided five over twelve now by the rate of how long person two can work, which is one-eigth of the total fence, which would be . Therefore, person two would have to work for a remaining three and one-third hours to paint the fence, and they took five and one-third hours in total.
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